As I pointed out in the comments, the story in Action #304 is a wholesale swipe of an identically-named story that had appeared in Action #220, seven years earlier. Both stories start with Clark being pulled upward in a stairwell by a mysterious ray, then almost getting caught by Lois floating in his office. Both stories feature Superman competing on an alien world for an energy crystal trophy, and failing miserably. The ending in Action #220 is different; it turns out that Superman had been affected by a piece of Kryptonite in the stadium, and that the winner of the contests, Brunno, had actually been a robot controlled by crooks who wanted the energy crystal.
In Detective #260 (October 1958), Batman is summoned by aliens to solve The Mystery of the Space Olympics. He competes in events such as rocket-racing, skeet-shooting (artificial meteors are the target), and anti-gravity boxing. He wins all the contests, actually surprising himself at how easy it was (kind of the reverse of the Superman story). But the Plutonians discover that he has been given assistance by the host Venusians:
However, it turns out to be a plot by the Plutonians to provoke a war with Venus, which Batman exposes in the nick of time.
In Jimmy Olsen #5, The Boy Olympics takes place. Jimmy learns that a competitor of the Daily Planet is about to go under, costing the jobs of a bunch of young paperboys. He gets the brilliant idea of having the kids put on a show. It's not an Olympics per se, just a bunch of thrilling stunts which Superman helps to arrange. The humor in the story arises from Jimmy's attempts to prevent Perry White from figuring out he's helping a competitor to his own paper. But in the end it turns out that Perry himself had helped out as well.
The Olympics theme also pops up in Teen Titans #4:
Wonder Girl lets us know a little bit of Olympic Trivia:
Considering that women weren't even allowed to be spectators at the original Olympics (possibly because the men were competing naked), that seems highly unlikely.
In the story, the Teen Titans are being asked to locate an Olympic hopeful named Davey Bradley. It turns out that Davey has the sports parent from hell: his dad had also qualified for the Olympics, but an auto accident ruined his chance of winning a gold medal. Meanwhile, a mysterious group called Diablo is trying to cause trouble at the games by provoking incidents.
In the story's climactic scene, the Teen Titans are stuck to the Olympic rings as shown on the cover, with Speedy about to light the rings on fire. Davey, who's been practicing his running in secret at the stadium that night sees the problem. He outruns Kravik, his likely chief competition for a medal, to prevent Speedy from shooting any more arrows at the Titans.
In the actual Olympic competition the next day, something of a surprise happens:
It's a nice little story. As an aside, Speedy was supposed to light the Olympic rings at the opening ceremony, but as Wonder Girl had largely destroyed them, his participation was canceled. Oddly enough, in 1992, an archer did start the Olympic Games at Barcelona:
One of my favorite Olympic moments ever.
Adventure #277 (October 1960) featured The Underwater Olympics. Aquaman and Aqualad get the idea after seeing two whales racing, and decide to assemble competing teams of fish from the Atlantic and Pacific, respectively. They do not have a torch-lighting ceremony, but they do have the entry parade:
At first, Aquaman's Atlantic team seems to be winning all the medals, but then something surprising happens. Aqualad's fish start catching up. And in the finale, Aquaman makes an astonishing mistake by not racing through a patch of seaweed, so:
Of course, because they have told us throughout the story that this would be a big upset and that it couldn't possibly be happening, we know that there's a surprise ending in the works. It turns out that Aquaman's team had sandbagged on purpose. Aquaman had spotted a Kryptonite meteor hidden in the seaweed and knew that Horval, an unscrupulous salvage man, would retrieve it if he saw it. So Aquaman had intentionally avoided the Kryptonite rather than have Horval, who was observing the contest intently, discover the meteor and sell it to criminals. A-man gets a little self-congratulatory here:
But overall it's an excellent story.
In Wonder Woman #90 (July 1957), we get yet another story entitled, The Interplanetary Olympics. Wondie receives the obligatory invitation, and finds herself competing against the Wonder Woman of Mercury, Venus and Jupiter, each better equipped to handle their home planets than she is, and yet she defeats them all.
Mystery In Space #39 (Aug-Sept 1957) featured The Solar Olympics of 3000 AD. A young Olympic hopeful is shocked to discover that his hero, an Olympic decathlete, is assisting an alien invasion of Earth. But fortunately the former champ is just trying to fool the aliens, and together they escape, getting good training for the tryouts coming up:
